60 On the iLnergetics of the Induction Balance. 



III. Comparison of an Inductance with a Capacity. 

 Maxwell's method *: — 



U 1 = U 2 = U 4 =0; T 1 =T 3 = T 4 =0. 



^- = E», .-. ^ 2 =EoR 3 . 



Rl R-i ^3 



Rimington's modification t : — 

 As before, T 9 U 



' 2. = 3 

 t| R 4 



Pirani's method { : — 



U^U^IL^Q; T 1 = T 2 = T 3 = 0. 



T 4 -U 4 =0, .-. fe=n 2 



C 



4 



This is a very interesting case. Three of the arms are 

 non-inductive resistances, hence, for a balance, the impulsive 

 effect of the fourth arm must vanish. By Heavisides 

 theorem (7) this happens when the energies are equal. 



§ 5. Equation (9) is, as is to be expected, of the same form 

 as the ordinary condition for steady balance with non-inductive 

 resistances; for, if H represents the heat developed in any 

 given time, we may put the condition H 1 R4=R 2 R3 in the 

 form 



Hi _ H 3 H 2 _ H 4 n 9 s 



R 2 RT R x R 3 ' lL ~ j 



where, instead of energies stored, we now have energies 

 dissipated. 



The form is so simple that one naturally suspects the possi- 

 bility of a more direct method of deducing it. It is, perhaps, 

 suggestive that it represents dimensionally the equalization 

 of mechanical momenta, thereby determining the distribution 

 of energy in the field conditioned by the mechanical equi- 

 librium of the current indicator ; but, until more is known 

 regarding the nature of the processes of storing and dissipating 

 energy in electrical phenomena, its true dynamical inter- 

 pretation must necessarily remain obscure. 



* Clerk Maxwell, ' Electricity and Magnetism ' (3rd. ed.) ii. § 778, 

 p. 425. 



t E. C. Kimington, Phil. Mag. July 1887. 



X Cf. C. H. Lees, Phil. Mag. [6] xviii. p. 432 (1909). J, P. Kuenen, 

 Phil. Mag. [6] xix. p. 439 (March 1910). 



